Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian
type: Item
instance of: scholarly article
title: Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian
zbMATH Open document ID: 1095.11033
author: Edward F. Schaefer
author: Joseph L. Wetherell
published in: Journal of Number Theory
publication date: 2006-03-08T00:00:00Z
review text: The authors describe an algorithm for computing the Selmer group of an isogeny between Abelian varieties. This algorithm applies when there is an isogeny from the image Abelian variety to the Jacobian of a curve [see also \textit{E. F. Schaefer}, Math. Ann. 310, 447--471 (1998; Zbl 0889.11021)], and extends the set of tools we have for computing Selmer groups. The use of auxiliary Jacobian simplifies the determination of locally trivial cohomology classes. As an application, they compute the Mordell-Weil group \(J_C(\mathbb Q)\) (where \(C\) denotes the smooth plane curve \(x^4+ (y^2+ 1)(x+ y)= 0\)) and use a Chabauty argument to determine the set \(C(\mathbb Q)\).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 11G35
Mathematics Subject Classification ID: 14G25
zbMATH DE Number: 5009842
zbMATH Keywords: Selmer group
zbMATH Keywords: isogeny
zbMATH Keywords: Abelian variety
zbMATH Keywords: Jacobian variety
zbMATH Keywords: Galois cohomology
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.11.014
OpenAlex ID: W2001187496
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cites work: Q3741712
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DOI: 10.1016/J.JNT.2004.11.014
description: scientific article; zbMATH DE number 5009842